While I was reading a book on basic vectors I struck a question that when we define resultant vector of sum of vectors is the vector joining the tail of one vector to head of other vector. But why do we join it? because how do we prove that it is the resultant vector?
And sorry for that silly doubt
On
The real reason why when we add two vectors we do not place them head to tail or vice versa is because, the angle θ between the two vectors won't be correct...
In the sense that when we use the resultant vector formula ie,.
$\sqrt{A^2 + B^2 + 2AB*cos θ}$
the value of θ will not be correct and therefore the sum will be wrong As for the proof question take a look at these diagram....
From a glimpse at this image we can see that the two vectors get flipped and place in such a way to form a parallelogram the diagonal of this parallelogram will be the resultant vector
and for a proper mathematical proof to the parallelogram kindly reference:
That way the resultant vector is the vector whose components are the sums of the individual components.